The existence of a new feebly interacting scalar or pseudo-scalar
particle, \(X\) , is foreseen in several BSM scenarios. If \(X\)  decays to
invisible particles or lives long enough to decay outside the
detector, the signature of a \(K^{+}\rightarrow \pi ^{+}X\)  decay is the
same as that of the \(K^{+}\rightarrow \pi ^{+}\nu \bar{\nu }\)  decay. The
two-body decay \(K^{+}\rightarrow \pi ^{+}X\)  would result in a peak in
the reconstructed \(m^2_{\rm miss}\)  distribution, centred at the
squared value of the \(X\)  mass, \(m_{\rm X}^{2}\) . Using the event
sample selected in the \(K^+\rightarrow \pi ^+\nu \bar{\nu }\)  measurement, a search for a peaking
signal in the 2016–2018 data set is performed following the procedure
detailed in [1]}. The width of a signal peak is
determined by the resolution of the \(m^2_{\rm miss}\)  observable, which
decreases monotonically from \(0.0012\text{~GeV}^{2}/c^{4}\)  at
\(m_{\rm X}=0\)  to \(0.0007\text{~GeV}^{2}/c^{4}\)  at
\(m_{\rm X}=260\text{~MeV}/c^{2}\) .
